Medical Sciences: cram pack

Formula sheets, the key method steps for every topic and 14 practice problems, with full solutions at the back.

New problemsBack to the course

In the print window, choose “Save as PDF” to keep a copy on your device.

1Formulas and methods

Arterial blood gas interpretation

Normal ranges
pH 7.35–7.45, PaCO₂ 35–45 mmHg (4.7–6.0 kPa), HCO₃⁻ 22–26 mmol/L
ROME
Respiratory: PaCO₂ opposite to pH; Metabolic: HCO₃⁻ equal to pH
Winter’s formula
PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2
Metabolic alkalosis
PaCO₂ ≈ 0.7·HCO₃⁻ + 21
Anion gap
AG = Na⁺ − (Cl⁻ + HCO₃⁻) ≈ 8–12
Albumin-corrected gap
AG + 2.5·(4.0 − alb g/dL) = AG + 0.25·(40 − alb g/L)
Delta ratio
(AG − 12)/(24 − HCO₃⁻)
P/F ratio
PaO₂/FiO₂
Alveolar gas equation
PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8
Serum osmolality
2·Na⁺ + glucose + urea (2·Na⁺ + glucose/18 + BUN/2.8)

Method

  1. Read the pH: below 7.35 is acidosis, above 7.45 alkalosis.
  2. Find the value that explains it: PaCO₂ moving opposite to the pH is respiratory, HCO₃⁻ moving with the pH is metabolic.
  3. Look at the other value: normal means uncompensated, abnormal in the compensating direction means partial compensation, and a normal pH with both abnormal means full compensation.
  4. In a metabolic acidosis, compare PaCO₂ with Winter’s formula, 1.5·HCO₃⁻ + 8 ± 2, and calculate the anion gap Na⁺ − (Cl⁻ + HCO₃⁻).
  5. Check a high anion gap with the delta ratio and, when albumin is low, with the corrected gap.

ECG rhythm strip interpretation

Paper (25 mm/s, 10 mm/mV)
1 small box = 0.04 s, 1 large box = 0.20 s, 10 mm = 1 mV
Heart rate, regular rhythm
300 ÷ large boxes = 1500 ÷ small boxes = 60 ÷ RR (s)
Heart rate, irregular rhythm
QRS complexes in 6 s × 10
Normal PR interval
0.12–0.20 s
Normal QRS duration
< 0.12 s
QTc (Bazett)
QT/√RR
QTc (Fridericia)
QT/∛RR
QTc (Framingham)
QT + 154·(1 − RR)
Sinus rates
bradycardia < 60, normal 60–100, tachycardia > 100 /min
Escape rates
junctional 40–60, ventricular 20–40 /min
Fast rhythms
SVT 150–250 /min (narrow), VT > 100 /min (wide)

Method

  1. Rate: for a regular rhythm divide 300 by the large boxes or 1500 by the small boxes between two R waves; for an irregular rhythm count the QRS complexes in 6 seconds and multiply by 10.
  2. Rhythm: compare the R–R intervals. Equal is regular; a repeating pattern is regularly irregular; no pattern at all is irregularly irregular.
  3. P waves: is there an upright P wave in lead II before every QRS, all alike? Look for fibrillatory or sawtooth waves, inverted P waves and P waves without a QRS.
  4. PR interval: from the start of P to the start of the QRS, normally 0.12–0.20 s and constant. Watch whether it lengthens, stays fixed before a dropped beat, or varies at random.
  5. QRS duration: below 0.12 s is narrow; 0.12 s or more is wide. Then name the rhythm, and for the QT use QTc = QT/√RR (Bazett) with times in seconds.

Evidence-based practice statistics

Sensitivity and specificity
Se = a/(a + c), Sp = d/(b + d)
Predictive values
PPV = a/(a + b), NPV = d/(c + d)
Accuracy
(a + d)/n
Likelihood ratios
LR+ = Se/(1 − Sp), LR− = (1 − Se)/Sp
PPV at prevalence p
Se·p / (Se·p + (1 − Sp)(1 − p))
Odds
odds = p/(1 − p); p = odds/(1 + odds); post-test odds = pre-test odds × LR
Risk measures
RR = EER/CER, ARR = CER − EER, RRR = ARR/CER
Number needed to treat
NNT = 1/ARR, rounded up; NNH = 1/(EER − CER)
Odds ratio
OR = ad/(bc)
Incidence rate
new cases / person-time

Method

  1. Draw the 2 × 2 table and label a, b, c and d before you calculate.
  2. Read sensitivity and specificity down the columns, predictive values along the rows.
  3. For another prevalence, imagine 10 000 people and fill the table with Se, Sp and the prevalence.
  4. For a likelihood ratio, convert the probability to odds, multiply, and convert back.
  5. For a trial, find EER and CER first; then RR = EER/CER, ARR = CER − EER and NNT = 1/ARR rounded up.

2Practice problems

1.Human anatomyMedium

Which structure produces most of the cerebrospinal fluid?

  1. APia mater
  2. BArachnoid granulations
  3. CPineal gland
  4. DChoroid plexus
2.Human anatomyHard

Which coronary artery most often supplies the sinoatrial (SA) node?

  1. ARight coronary artery
  2. BLeft main coronary artery
  3. CLeft anterior descending artery
  4. DCircumflex artery
3.Human physiologyMedium

Cardiac output equals heart rate multiplied by:

  1. AStroke volume
  2. BBlood pressure
  3. CEjection fraction
  4. DPeripheral resistance
4.Human physiologyHard

According to the length–tension relationship, why does a skeletal muscle fibre produce less force when overstretched?

  1. AActin and myosin overlap less, so fewer cross-bridges form
  2. BCalcium is no longer released from the sarcoplasmic reticulum when stretched
  3. CThe muscle runs out of ATP when stretched
  4. DThe neuromuscular junction stops working
5.MicrobiologyMedium

In which phase of the bacterial growth curve do the cells divide at their fastest constant rate?

  1. ADeath phase
  2. BLog (exponential) phase
  3. CLag (adaptation) phase
  4. DStationary (plateau) phase
6.MicrobiologyHard

Why is Chlamydia trachomatis usually diagnosed with nucleic acid amplification tests instead of routine culture on agar?

  1. AIt is too large to grow on agar plates
  2. BIt dies immediately in the presence of oxygen
  3. CIt is a virus and has no DNA
  4. DIt is an obligate intracellular bacterium that cannot grow on ordinary media
7.PharmacologyMedium

Why are many drugs started at lower doses in older adults?

  1. ALower doses are cheaper for older patients
  2. BOlder adults absorb no drugs from the stomach
  3. COlder adults always weigh more than younger adults, so drugs last longer
  4. DKidney and liver clearance often decline, and sensitivity to drugs increases
8.PharmacologyHard

Why is strict aseptic technique and a limited hang time needed for propofol infusions?

  1. APropofol breaks down into a toxic gas after a few hours
  2. BLight exposure changes propofol into an opioid
  3. CIts lipid emulsion lets bacteria grow if it is contaminated
  4. DPropofol becomes more potent the longer it hangs
9.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 12 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 12 mmol/L
PaCO₂ = mmHg
10.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 24% oxygen shows PaO₂ 53 mmHg (7.1 kPa) and PaCO₂ 45 mmHg (6.0 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 24%PaO₂ 53 mmHg (7.1 kPa)PaCO₂ 45 mmHg (6.0 kPa)
A–a gradient = mmHg
11.ECG rhythm strip interpretationMedium
II25 mm/s · 10 mm/mV

Measure the QT interval and the R–R interval on this regular lead II strip, then calculate the rate-corrected QTc with Fridericia’s formula QTc = QT/∛RR (both in seconds). Give the answer in seconds to three decimals.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
QTc = s
12.ECG rhythm strip interpretationHard
II25 mm/s · 10 mm/mVsinus bradycardiaasystoleidioventricular rhythmjunctional rhythm

Identify the rhythm on this lead II strip. Click your answer.

lead II, 25 mm/s, 10 mm/mV1 small box = 0.04 s, 1 large box = 0.20 sstrip length 6 s
  1. 1sinus bradycardia
  2. 2asystole
  3. 3idioventricular rhythm
  4. 4junctional rhythm
13.Evidence-based practice statisticsMedium
casescontrolsexposed157227abnot exposed53193cd

Practice exercise (made-up values, not clinical guidance). A case-control study compares 210 patients with a disease (cases) and 420 people without it (controls). The table shows how many in each group were exposed to a risk factor. Find the odds ratio OR for the exposure. Round to two decimal places.

a = 157b = 227c = 53d = 193
OR =
14.Evidence-based practice statisticsHard
pre-test5%post-test?p′LR−

Practice exercise (made-up values, not clinical guidance). A patient has a pre-test probability of 5% for a disease. A test with sensitivity 63% and specificity 93% comes back negative. Find the post-test probability p′ of the disease as a percentage. Round to one decimal place.

pre-test 5%Se = 63%Sp = 93%negative
p′ = %

3Solutions

1.Human anatomy

Answer: D · Choroid plexus

Why this is the answer

The choroid plexus in the ventricles secretes most CSF. CSF is reabsorbed into venous blood through the arachnoid granulations.

Answer

D · Choroid plexus
2.Human anatomy

Answer: A · Right coronary artery

Why this is the answer

The SA nodal artery arises from the right coronary artery in roughly 60% of people and from the circumflex artery in the rest.

Answer

A · Right coronary artery
3.Human physiology

Answer: A · Stroke volume

Why this is the answer

CO = HR × SV. At rest about 70 beats/min × 70 mL ≈ 5 L/min.

Answer

A · Stroke volume
4.Human physiology

Answer: A · Actin and myosin overlap less, so fewer cross-bridges form

Why this is the answer

Maximum force occurs at an optimal sarcomere length with best filament overlap. Overstretching reduces overlap; too short a length makes filaments collide.

Answer

A · Actin and myosin overlap less, so fewer cross-bridges form
5.Microbiology

Answer: B · Log (exponential) phase

Why this is the answer

After the lag phase of adjustment, cells enter the log phase and grow exponentially. Growth stops in the stationary phase as nutrients run out and waste builds up.

Answer

B · Log (exponential) phase
6.Microbiology

Answer: D · It is an obligate intracellular bacterium that cannot grow on ordinary media

Why this is the answer

Chlamydia replicates only inside host cells, so it cannot be grown on agar. NAATs such as PCR on urine or swabs are sensitive and are the standard diagnostic test.

Answer

D · It is an obligate intracellular bacterium that cannot grow on ordinary media
7.Pharmacology

Answer: D · Kidney and liver clearance often decline, and sensitivity to drugs increases

Why this is the answer

Ageing reduces kidney function, changes body composition and often slows liver metabolism. Many drugs also have stronger effects on the ageing brain, so doses are started low and increased slowly.

Answer

D · Kidney and liver clearance often decline, and sensitivity to drugs increases
8.Pharmacology

Answer: C · Its lipid emulsion lets bacteria grow if it is contaminated

Why this is the answer

Propofol is formulated in a soybean oil emulsion, which is a good growth medium for bacteria. Contaminated propofol has caused sepsis, so it is handled aseptically and tubing and containers are changed at set intervals.

Answer

C · Its lipid emulsion lets bacteria grow if it is contaminated
9.Arterial blood gas interpretation

Answer: PaCO₂ = 26 mmHg

Expected compensation: in metabolic acidosis Winter’s formula predicts PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2 mmHg; a measured value above that range points to an additional respiratory acidosis, below it to an additional respiratory alkalosis. The anion gap AG = Na⁺ − (Cl⁻ + HCO₃⁻), normally about 8–12 mmol/L, separates high-gap from normal-gap metabolic acidosis; low albumin hides a high gap (add 2.5 per g/dL that albumin is below 4.0). The delta ratio (AG − 12)/(24 − HCO₃⁻) between about 0.8 and 2 fits a pure high-gap acidosis (some texts use 1 instead of 0.8), below that an added normal-gap acidosis, and above 2 an added metabolic alkalosis.

Winter’s formula

PaCO₂ = 1.5·12 + 8 = 26 mmHg
range: 24–28 mmHg

Answer

PaCO₂ = 26 mmHg
10.Arterial blood gas interpretation

Answer: A–a gradient = 61.87 mmHg

Derived values: calculated serum osmolality is 2·Na⁺ + glucose + urea with all values in mmol/L (2·Na⁺ + glucose/18 + BUN/2.8 with glucose and BUN in mg/dL); normal is about 275–295 mOsm/kg. The P/F ratio is PaO₂ divided by FiO₂ as a fraction. The alveolar oxygen pressure is PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 mmHg at sea level, and the A–a gradient is PAO₂ − PaO₂.

Alveolar oxygen

PAO₂ = 0.24·713 − 45/0.8 = 171.1 − 56.25 = 114.9 mmHg

Gradient

A–a = 114.9 − 53 = 61.87 mmHg

Answer

A–a gradient = 61.87 mmHg
11.ECG rhythm strip interpretation

Answer: QTc = 0.48 s

QT and QTc: the QT interval runs from the start of the QRS complex to the end of the T wave. It shortens as the heart rate rises, so it is corrected for rate with the R–R interval in seconds: Bazett QTc = QT/√RR and Fridericia QTc = QT/∛RR. Bazett is the formula most textbooks use; it over-corrects at fast rates, where Fridericia is preferred. Limits differ between references: a QTc above about 0.45 s in men or 0.46 s in women is usually called prolonged, and above 0.50 s markedly prolonged.

Measure

QT = 12 × 0.04 = 0.48 s
RR = 25 × 0.04 = 1.00 s

Fridericia’s formula

QTc = 0.48/∛1.00 = 0.48/1 = 0.48 s

Answer

QTc = 0.48 s

Above the usual limits for both men (about 0.45 s) and women (about 0.46 s): prolonged. (480 ms)

12.ECG rhythm strip interpretation

Answer: idioventricular rhythm

More ventricular rhythms: torsades de pointes is a polymorphic ventricular tachycardia, usually 150–250/min, in which the wide complexes change in height and twist around the baseline, pointing up for a few beats and then down. Textbooks link it to a prolonged QT interval, and magnesium sulfate is the drug resuscitation guidelines name for it. An idioventricular rhythm is a ventricular escape rhythm: regular, wide QRS (0.12 s or more), no P waves, at 20–40/min (an accelerated idioventricular rhythm runs at 40–100/min). Monomorphic VT has identical wide complexes at more than 100/min. VF is chaotic, without any repeating complex.

Five steps

1. Rate: R–R = 54 small boxes, 1500 ÷ 54 ≈ 28 per minute.
2. Rhythm: regular, every R–R is 2.16 s.
3. P waves: none identifiable.
4. PR interval: not measurable.
5. QRS: 0.18 s, wide (0.12 s or more) and bizarre, with the T wave pointing the other way.

Interpretation

idioventricular rhythm

Answer

idioventricular rhythm

An idioventricular rhythm is an escape rhythm: the ventricles take over because the pacemakers above them have failed.

13.Evidence-based practice statistics

Answer: OR = 2.52

Likelihood ratios and risk measures: LR+ = sensitivity/(1 − specificity), LR− = (1 − sensitivity)/specificity. In a trial, EER and CER are the event rates with and without treatment: RR = EER/CER, ARR = CER − EER, RRR = ARR/CER and NNT = 1/ARR, rounded up. In a case-control study only the odds ratio OR = ad/(bc) can be used. An incidence rate = new cases/person-time.

Odds of exposure

cases: 157/53 = 2.962
controls: 227/193 = 1.176

Odds ratio

OR = (157·193)/(227·53) = 2.519 ≈ 2.52

Answer

OR = 2.52

OR above 1: exposure is more common among the cases.

14.Evidence-based practice statistics

Answer: p′ = 2.1 %

Predictive values depend on prevalence: PPV = Se·p/(Se·p + (1 − Sp)(1 − p)) and NPV = Sp(1 − p)/(Sp(1 − p) + (1 − Se)p). With likelihood ratios: pre-test odds = p/(1 − p), post-test odds = pre-test odds × LR, probability = odds/(1 + odds). For a population of N, true positives = N·p·Se and false positives = N·(1 − p)·(1 − Sp). NNT = 1/(CER × RRR), rounded up.

Likelihood ratio

LR− = (1 − 0.63)/0.93 = 0.3978

Pre-test odds

0.05/(1 − 0.05) = 0.05263

Post-test odds

0.05263·0.3978 = 0.02094

Post-test probability

p′ = 0.02094/(1 + 0.02094) = 0.02051 ≈ 2.1%

Answer

p′ = 2.1%

ExamProblems · examproblems.com/courses/medical-sciences